Abstract: The Finite Difference Time Domain (FDTD) method applied in sound scattering prediction was validated firstly,then the shape of 6-and 12-order-stepped sound diffusers consisted of multiple periods were optimized respectively using hybrid method combined FDTD with immune genetic algorithm.Two optimization ways were used in the present study for comparison.One is to directly optimize the shape of diffusers consisted of repeated periods,and the other is to conduct the optimization for single period diffuser before period repetition.The results show diffusers with better diffusion performance can be obtained in the first optimization way;the single period diffuser with the optimal shape will not remain the best diffusion performance when repeated for some periods,on the contrary,some with non-optimal shape for a single period could achieve better diffusion performance than the former when certain periods were repeated.The diffusion performance would be improved when increasing diffuser's order and decreasing diffuser's repeat periods under the same overall diffuser's width condition.It was concluded that the way to achieve best diffusion performance for periodic diffusers was optimizing shape of periodic diffusers with higher order directly.